Charge released from rest near a grounded conductor

1. The problem statement, all variables and given/known data
A charge q of mass m is released a distance d from a semi-infinite grounded conductor. How long will it take the charge to reach the conductor?

So I tried this using the method of images, and I can easily find the force on the charge a distance d away:

d is a constant here: instead, write the force as a function of the variable z (the variable distance to the conductor). Then, as an intermediate step, can you get an equation for the velocity dz/dt of the charge as a function of z?